11Complex global value chains are those involving more than two countries and imply that a country 12 imports products as capital goods or intermediate inputs to the production of its exports. When tracing 13 the life-cycle greenhouse gas (GHG) emissions of traded products, for example for border carbon 14 adjustments, such emissions are counted at each border crossing. The prevalence and dynamics of this 15 phenomenon have been poorly understood. This paper shows that GHG emissions associated with the 16 production of imports used for producing exports have risen rapidly from 1995, peaking in 2012 and 17 declining slightly to 2016. They now constitute a total of 4.4 PgCO 2 equ. or 10% of global emissions. The 18 most important exported products in terms of emissions associated with imported inputs are chemicals, 19vehicles, machinery, and information and communications technology (ICT). Crude petroleum, iron and 20 steel, chemicals, and ICT components are the imported products being used for this export production. 21A driver analysis indicates that in industrialized countries, the declining domestic value added in exports 22 and increasing share of exports in GDP have contributed most to this development, while in emerging 23 economies, the growth of GDP itself has been an important driving factor, while declines in the energy 24 intensity of export production have provided a weak counterbalance. The importance of transiting 25 carbon raises questions of how climate policies affect industrial competitiveness and how border tax 26 adjustment would account for such emissions. 27 28 2 Keywords: Emissions embodied in trade; carbon footprint; multiregional input-output analysis; 29 EXIOBASE; trade in value added (TiVA); index decomposition; complex global value chains. 30 31